Poission equation, spherical harmonics, looking for reference

Click For Summary

Discussion Overview

The discussion revolves around finding references for the derivation of a specific formula related to the Poisson equation and spherical harmonics, particularly in the context of electrostatics. Participants seek detailed descriptions and derivations from established texts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant requests a derivation of a specific formula from a linked image, suggesting that Jackson's electrodynamics book may contain the information but is unable to locate it.
  • Another participant explains that the electrostatic potential is defined in terms of charge density and suggests integrating over the charge density to derive the necessary formula.
  • A different participant recommends Section 4.2.5 in Franklin's "Classical Electromagnetism" as a potential reference for the derivation.
  • Another suggestion is made to consult Weinberger's "A First Course in Partial Differential Equations," specifically the chapter on Legendre and associated functions, indicating that similar treatments can be found in other texts on partial differential equations.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on a single reference, with multiple suggestions offered instead. The discussion remains unresolved regarding the best source for the derivation.

Contextual Notes

Participants reference various texts, indicating that the derivation may depend on different interpretations or approaches to the Poisson equation and spherical harmonics. There is no indication of which reference might be the most authoritative or comprehensive.

Derivator
Messages
147
Reaction score
0
Hi folks,

I'm looking for a derivation of the following statement (formula 76)
http://img845.imageshack.us/img845/1550/screenshot4op.png

Do you know any reference, where I can find a bit more detailed description? I reckon, you can find it in Jackson's electrodynamic book, but I couldn't find it.derivator
 
Last edited by a moderator:
Physics news on Phys.org
Well, if you take a look at the original definition of the electrostatic potential, which is basically given by something proportional to q/|r-r'|. In order to get q, you have to integrate over the charge density rho which is given in your text. The factor of 1/|r-r'| is also given there, so you just have to combine those two and calculate.
 
Try Sec. 4.2.5 in Franklin "Classical Electromagnetism".
 
Weinberger "A first Course in Partial Differential Equations" treats this in his chapter on Legendre and associated functions p 192 ff

But any good book on partial diffs should have a similar treatment.
 

Similar threads

  • · Replies 36 ·
2
Replies
36
Views
4K
  • · Replies 11 ·
Replies
11
Views
16K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 25 ·
Replies
25
Views
3K